Are there other Chinese cities besides 厦门 and 澳门 which end in 门 and what does 门 mean in this context?
The name was formerly written using the Chinese characters meaning "Lower Gate".
Lower Gate should equate to 下门.
When its port prospered under the Qing, the name was considered unrefined and changed to homophonous characters meaning "Mansion Gate".
Mansion Gate is the current name 厦门.
The present Chinese name (Chinese: 澳門; pinyin: Àomén; Cantonese Yale: Oumún) means "Bay Outlet".
Gate exists in British English also but with a very different meaning (road), think:
and second similar idea is found on the wiki page for:
George R. Stewart theorized, in his book Names on the Globe, that Hellespont originally meant something like "narrow Pontus" or "entrance to Pontus", "Pontus" being an ancient name for the region around the Black Sea, and by extension, for the sea itself.
A place's name ended with 门 (gate/door) is usually an entry point of a city, providence or region.
The first part of the name may not even necessary be the providence's name. For example, 鲤鱼门 (Lei Yue Mun) is the east gate of Victoria Harbour in Hong Kong, but it isn't called Victoria Harbour Gate, because the name Victoria Harbour didn't exist 200 years ago.
As for why it is called 鲤鱼门 (Lei Yue Mun), no one know for sure. May be it came from the legend of 鯉躍龍門 (A carp that can jump over the top of Dragon Gate Fall would turn into a dragon), maybe it's because the terrain there looked like a 鲤鱼 (carp), or may be it was famous for carp fishing.
They are just names. But some stories can be found for them.
The name of 厦门 comes from 厦门城 (AD 1387). 厦门城 means “国家大厦之门”--the entrance of the nation 1.
And 澳门 comes from 濠镜澳, which means 盛产蚝且水域如镜的港湾 2.
Basically, 门 means gate/port when is found in a city's name. But sometimes it is from some historical events/location.